Suspension insulator



MaylS, 1934. 'E'EARNOLD 1,958,880

SUSPENS ION INS ULATOR Fil'ed March 19, 1932 5 Sheets-Sheet 1 WITNESSES: INVENTOR Edwin A. flrnold ATT NEY y 5,1934. E. E. ARNOLD 1.958380 SUSPENS ION INSULATOR Filed March 19, 1932 3 Sheets-Sheet 2 WITNESSES: l INVENTOR aWl'H fifll 'nold flfl. A Mm BY W M ATTORNEY Patented May 15, 1934 I UNITED, STATES PATENT OFFICE SUSPENSION INSULATOR Application March 19, 1932, Serial No. 599,903

Claims.

My invention relates to suspension insulators and has particular relation to a specific structure thereof for enabling them to successfully withstand, without mechanical or electrical I breakdown, tensile forces of a magnitude heretofore unattained.

Suspension insulators. widely known and employed at the present time, vary considerably in structure, but they all comprise, essentially, a dielectric member of suitable material, such as porcelain or glass, a cap member suitably secured to the outside surface of the dielectric member for supporting it, and a load supporting member or stud suitably secured within a cavity in the dielectric member.

As far asis known, all of the suspension in-l' sulators in use at the present time are incapable of attaining their maximum strength, under tension, because of the unequal distribution of compressive stresses in the dielectric member and the cementitious material ordinarily employed to secure the load supporting stud within the cavity of the dielectric member.

The problem of overcoming the unequal distribution of stresses in the dielectric member and the cementitious material has been recognized and an attempt made to solve it in U. S. Patent 1,822,485 to K. A. Hawley. This patent discloses a suspension insulator which is provided with a load supporting stud having a working surface within the cavity of the dielectric member of spherical contour. The principle or theory for such contour of the working surface on the stud is that for a given axial movement of the stud, relative to the cementitious material interposed between the working surface of the stud and the walls of the cavity in the dielectric member, a compressive movement of the cementitious material, in a directlon perpendicular to the working surface at any point thereon, occurs which is proportional to the sine of the angle subtended by a line having the same slope as a point on the working surface of the stud, and by the longitudinal axis 0f the Stud.

The solution disclosed by the patent is to vary the thickness of the cementitious material perpendicular to the working surface of the stud at different given points in proportion to the sine of the angle subtended by the line of identical slope as the various points on the working surface, and by the longitudinal axis of the stud, so that the percent deformation of the cementitious material is the same in all .portions thereof.

.cavity having substantially straight wall surf A variation of the thickness of the cementitious material in accordance with such principle necessitates, however, an arcuate undercut surface for the walls of the cavity in the dielectric member. The endeavor of insulator manufacturers has been to avoid employing a recessed or undercut cavity for the reason that shearing stresses in the dielectric member incident there- 'to which would reduce the strength of the insulator itself; are obviated, as well as that it is both diilicult and expensive to secure a load supporting stud within a cavity of this character.

The patent discloses a cavity having wall surfaces which are substantially straight, and, therefore, the maximum equalization of stress obtainable by employing a working surface on the stud of spherical contour is not secured because of the disproportionate increases in the thickness of the cementitious material over that required at the various points. It is the purpose of my invention to solve the problem of unequal distribution of stresses in the cementitious material and the dielectric member of a suspension insulator, and obtain maximum equalization of compressive stresses in the cementitious material and the dielectric member while employing a cavity in the dielectric member having straight wall surfaces.

I have proceeded under an entirely different theory and principle from that disclosed in the patent to Hawley, as will be explained in detail hereinafter, and have devised a working surface for the load supporting stud of a suspension insulator which is different in contour from any contour previously known or devised. I have determined mathematically the nature of the curve or contour for the working surface of the stud, which will effect an equalization of compressive stresses in the cementitious material and the dielectric member when the stud is disposed in a faces, by equating the mathematical expression for the compressive stress along a horizontal'axis and that for the compressive stress along the vertical axis, caused by an increment dy of axial movement of the stud tending to separate it from the dielectric member, and solving the mathematical equation so obtained.

After the theoretical curve of the working surface of the stud is thus obtained, I empirically determine a curve of constant radius of curvature which conforms closely to the contour of the theoretical curve. I obtain the entire working surface of the stud by revoling this are or curve of constant radius of curvature through one comno plete revolution about the longitudinal axis of the stud.

between maximum and minimum tensile strength.

values obtained therefrom is a heretofore unattained minimum and also that a higher minimum tensile strength value is consistently obtained therefrom than heretofore.

It is, also, a more specific object of my invention to provide a working surface for the load supporting member or stud of a suspension insulator, which effects a heretofore unattained maximum equalization of stress in the median surrounding the working surface while employing a cavity in the dielectric member having substantiallystraight' wall surfaces.

It is a further object of my invention to provide a load supporting stud in a suspension insulator, of a character and for the purposes as above set forth, which is capable of being readily and cheaply manufactured on a commercial scale.

Qther objects of my invention will be apparent from the following theoretical discussion of the principles upon which my invention is based and the description of the structural details thereof given hereinafter, when read in connection with the accompanying drawings wherein:

Figure 1 is a view, in, transverse section, taken along the axis of an insulator, showing the structural details of one embodiment of my invention;

' Fig. 2 is a diagram which will be referred to in connection with the derivation of the theoretical curve upon which the contour of the working surface of the stud which I employ. is based; and

Fig. 3 is a diagram, showing to an exaggerated degree for purposes of clarity, the relation between the actual curve of the working surface of the stud and the-theoretical curve therefor, as well as the preferred proportionsof the various dimensions of a stud constituting a practical embodiment of my invention, and the relation between the inner working surface of the cap member to the working surface of the stud.

Referring to Fig. 1, the type of suspension insulator which I. employ comprises a dielectric member 2 of suitable material, such as porcelain,

a cap member 4, preferably of metallic nature, and a load-supporting stud 6. The dielectric member 2 is secured to the cap member 4 in any suitable manner, after centering the upwardly projecting cylindrical portion thereof within the cup-like receiving portion of the capmember 4.

A cruciform spacer 8, of fibrous or other suitable material, is interposed between the outer end of the cylindrical portion of the dielectric member 2, and the inner surface of the cap member 4 for the purpose of properly centering the cylindrical portion of the dielectric member with-v in the cap member 4, as fully described and claimed in my copending application, Serial No..

' I 505,066, filed December 27, 1930 and assigned to the Westinghouse Electric and Manufacturin Company.

A suitable cementitious material 9 fills the remaining space between the protruding inner- It is, therefore, an object of myinvention to so.

in a suitable manner, such as by sanding it, to

cause the material 9 to adhere thereto.

The stud 6 is suitably retained within the inner cavity 10 of the dielectric member by a quantity of cementitious material 14 interposed between the head 16 and shank 18 of the stud and the wall surfaces of the cavity. The wall surfaces of the cavity 10 are roughened in any suitable manner, preferably by sanding, for aiding in the adhesion of the cementitious-material 14 thereto. A cruciform spacer 12 is interposed between the end of the stud and the inner surface .of the cavity 10 whereby the stud fi-isproperlycentered within the cavity, as also described in my aboveidentified copending application;

A lubricating film 20 of suitable material, such as a pitch or gum, is interposed between the inner the purpose of permitting relativemovement between the stud and the cementitious material when the insulator is subjected to tensile forces tending to separate the stud from the dielectric member.

It will be observedth'at the cap member is provided with a surface of concave curvature facing the outer surface of the dielectric member whereas the working surface 24 on the head of the stud is of convex curvature facing the inner surface .of the walls of the cavity 10, The compressive forces, acting perpendicularly to the working surface 24 whenever an axial movement of the stud 6 with respect to the dielectric member 2 occurs, are, therefore, balanced by the compressive reaction forces created by a corresponding axial movement of the cap member 4 with respect to the dielectric member 2, in the manner described in U. S. Patent No. 1,802,704 to S. L. Case, assigned to the Westinghouse Elec trio and Manufacturing Company. The principle and reason underlying the cooperative relatiori of the working surface 24 and the inner surface of the cap member is, of course, that the porcelain or other dielectric material is thereby subjected almost entirely to compressive forces only. Because porcelain is possessed of its highest mechanical strength when under compression, the construction disclosed in the patent to Case enables the obtaining of an especially high mechanical strength in tension for the insulator.

The working surface on the head of the stud in the patent to Case is frusto-conical in nature, that is, the working surface has a constant slope with respect to the longitudinal axis of the stud.

Due to the fact that a working surface of constant slope is employed, there is an unequal distribution of the compressive stresses in the cementitious material andthe porcelain, interposed betweenthe working surface of'the head of the stud and the inner surface of the cap member, when the insulator is subjected totensile forces tending to separate the stud and the cap from the dielectric member. The maximum tensile strength of the insulator in the direction of the axis of the stud is therefore limited, due to the fact that the increments of peripheral area on the axis of the stud, effect per unit of area there- I creases as it approaches the shank of the stud, it

happens that the unit deformation of the porce-- lain or dielectric material at portions thereof opposite the increments of peripheral area on the 7 working surface most remote from the axis of the stud is greater, than other portions thereof opposite increments of peripheral area on the working surface which are closer to the axis of thestud. The tensile force which the insulator can successfully withstand without electrical breakdown and mechanical fracture is, therefore, dependent upon the compressive strength of only a small portion of the dielectric member instead of that of the major portion of the dielectric member.

I have devised an insulator which employs the principle disclosed in the patent to Case but which also employs a load-supporting stud having a working surface of entirely different nature, as well as a cap member having a different working surface, than that employed in the patent to Case, whereby the compressive stresses in the dielectric member are equalized and the major portion of the dielectric member rendered effective to resist tensile forces applied to the insulator, It is thus inevitable that insulators constructed in accordance with my invention should successfully attain tensile strengths of greater maximum, median, average and minimum values than those which insulators constructed merely in accordance with the patent to Case are capable of attaining.

The theory and basis for my invention can best be understood by referring to the diagram shown in Fig. 2 and following through the mathematical derivation of the algebraic expression for the theoretical curve upon which the working surface 24, which I employ, is based.

For purposes of the solution, the straight inner wall surfaces of the cavity 10, are assumed to, be parallel to the' longitudinal axis of the stud; Such assumption may be made because the taper of the walls is very slight. Coordinate axes are employed, one being designated y-axis and coinciding with the center line or longitudinal axis of the stud, and the other being designated x-axis (l) and coinciding with the lower extremity of the cementitious material 14 interposed between the stud and the wall surfaces of the. cavity in the dielectric member.

The radius of the shank of the stud is constant and is designated by the known quantity D. A hypothetical cylindrical neutral boundary of compressive forces is assumed to exist between the working surfaces on the stud and on the cap' member, for a reason which will be explained hereinafter, which boundary is concentric with respect to the axis of the stud and a radial distance r therefrom. This boundary is indicated by the line N which is in reality the intersection therewith of a plane common to the boundary and the axis of the stud.

It will be understood that the cylindrical neutral boundary indicated by the line N is that hypothetically thin cylindrical zone in which the compressive stresses set up by the stud and those become zero.

The distance from the intersection of the work-- ing surface and the shank of the stud to the lower extremity of the cementitious material 14 is designated yo, and although a specific value therefor is taken in the plottingof the curve shown in Fig. 2, it should be understood that such value is merely an arbitrary one taken for reasons hereinafter explained.

An axial movement dy of the stud 6 in a direction away from the dielectric member, such as would be caused when the-insulator is subjected to tension, is assumed. Obviously, .the working surface of the stud moves toward :r-axis (l) a distance dy at all points thereon so that the working surface shown in solid lines moves to the position shown by the broken line. Clearly, there is effected a compressive movement of the cementitious material as well as of the porcelain, as a result of such axial movement of the stud.

Assuming a compressive movement of the surrounding medium only in a directionparallel to :r-axis (l), the volume displaced by an 'axial movement dy of the stud may be expressed algebraically in terms of the increment of area abdc multiplied by the peripheral distance around the working surface. The increment of area abdc may be assumed to be a true parallelogram for the purposesof this solution, and its area is equal to the height dy thereof multiplied by the base dx, which is the increment of compressive movement in'the direction of :r-axis (l). The pe ipheral distance around the working surface at the point taken is obviously equal to 21r mul= tiplied by the coordinate distance .r. Thus, the mathematical expression for the volume V displaced in a direction parallel to :v-axis (1) may be expresed Assuming a compressive movement of the surrounding medium, upon an axial movement dy of the stud, only in a direction parallel to y-axis, the volume of surrounding medium displaced is obtained by multiplying the increment of area efhg by the peripheral distance at the point 6) around the working surface of the stud. The increment of area ejhg may also be assumed for the purposes of this solution to be a true parallelogram, and its area is", therefore, the height dz: multiplied by the base dy. The peripheral distance around the working surface at the point ef' is, of course, 21m, and thus the volume V of surrounding medium displaced may be expressed as Obviously, the two parallelograms abdc and cjhg are shown in Fig. 2 for purposes of clarity. It should be understood that the same increment of working surface extending around the periphery of the working surface of the stud is taken in order to obtain the volume V displaced thereby for compressive movement or deformation of. the surrounding medium; only in a direction parallel to .r-axis (1) and only in a direction parallel to y-axis.

It will be observed, therefore, that the volume V of surrounding medium displaced is the same in each case, namely, ZwiDdZ/(ZIE.

In order to'obtain the compressive stresses in a direction parallel to x-axis (1), and parallel to y-axis, it is necessary first to obtain, in each case, the mathematical expressions for the volumes of surrounding medium into which the increment of displaced volume V is moved.

' thetical boundary from the wall surface of the For the purposes of this solution, the hypothetical cylindrical neutral boundary of compressive forces indicated by the line N is assumed as that which would be created if the medium interposed between the working surfaces of the stud and the cap member were homogeneous, such as, for example, all cementitious material.

'Obviously, this is permissible because the distance of the actual neutral boundary of compressive forces from the wall surface of the cavity 10 bears a ratio to the distance 1' of the hypocavity proportional to the ratio which the modulus of elasticity of the cementitious material bears to that of the dielectric material. In other words, the distance of the hypothetical neutral boundary from the surface of the cavity 10, is greater, assuming a homogeneous surrounding medium of cementitious material, than the distance between the actual neutral boundary of the compressive forces'and the surface of the cavity 10, assuming a portion of the surrounding medium to be porcelain, because the dielectric material, such as porcelain, possesses a higher modulus of elasticity than does the cementitious material.

It simplifies the solution however, if the me-' dium surrounding the working surface of the stud is assumed to be homogeneous, and inasmuch as it is immaterial whether the actual neutral boundary of compressive forces is employed as a reference zone or whether the hypothetical neutral boundary is employed, I prefer to employ the hypothetical neutral boundary.

The volume of surrounding medium into which the increment of displaced volume V is moved in a direction parallel to :r-axis 1) is thus that of a, washer-like section of thickness dy, having an outer radius of curvature equal to r, (the radial distance from y-axis to the hypothetical neutral boundary) and an inner radius of curvature equal to the coordinate value x. The volume V1of this portion of the surrounding medium may be expressed mathematically as The compressive stress S, set up in a member or material is equal. generally speaking, to the unit deformation (1 of the material multiplied by its modulus of elasticity M.

Accordingly, therefore, the compressive stress Sx in the surrounding medium acting radially and expansively from the working surface on the stud, may be expressed mathematically by dividing the displaced volume V by the volume V1 of the surrounding medium into which it is displaced, and multiplying the quotient by the modulus of elasticity M of the cementitious material. In other words,

-The increment of displaced volume V when compressed into the surrounding medium only in a direction parallel to the y-axis, sets up a com-- Obviously, the volume V2 of surrounding medium to which the displaced volume V is displaced is that of a cylinder having a height a radius of curvature :r, and a .wall thickness (12'. Thus, the volume V2 mybe expressed The compressive stress S set up in the cementitious material as a result of the compression of a value V into the volume V2 thereof, may therefore be expressed by the equation:

In order to have an equalization of stresses caused by any increment of peripheral area on the working surface of the stud, the horizontal and vertical components thereof must be equal.

Thus, assuming Sx and Sy in Equations (1) and (II) to be equal, we have y Cancelling the constant M from each side of the equation, we have V dy ZXdx I V y Integrating, by calculus, each. side of the Equation (III) we have K log y=log G Thus,

Therefore,

K =yo Substituting, in Equation (1v) the value for K, thus obtained, we have Since the quantity 110 is variable, :c-axis (1) also is variable in position. Therefore, in order to obtain an expression for the curve of the working surface referred to a fixed :c-axis, :1:- axis (2), lying in'the plane passing through the intersection of the working surface and the shank of the stud is taken as the :c-axis to which the expression for the curve given in Equation (V) may be referred. Expressing the general value of the y-coordinate, based upon the 00- ordinate axes gj-axis and :r-axis (2), as y, we

may express Equation (V) as:

In other words,

, WE- ill y0( fl Equation (VI) is thus the general expression for the curve or contour of the working surface of the stud which will effect an equalization of compressive stresses in the surrounding medium upon a given axial movement of the stud, tending to separate the stud from the dielectric memher when a cavity in the dielectric having straight wall surfaces is employed. Theoretically, therefore, two increments of peripheral areas on working surface of the stud, which are different distances from the axis of the stud will effect the same stress in the surrounding medium. Thus,

since all portions of the surrounding medium,

that is, of the cementitious material and the strength for the insulator itself is effected.

It will be appreciated that the quantities yo and r in Equation (VI) may be assigned arbitrary values and the values of 1,! corresponding to various plus and minus values of :0 thereby determined. By assuming a plurality of sets of values for ya and r, and substituting for a: a plurality of different plus and minus values, based upon a ratio thereof with respect to the radius D, a plurality of curves may be obtained.

. One of these curves possesses the necessary contour to effect a simple ratio of dimensions of the head of the stud, with repect to the radius D of the shank. This curve is that which employs a value for ya equivalent to (rD) when r is equal to 2.5D.

The curve of the working surface of the stud; as shown in Fig. 2, is plotted on the basis of the equality of go and (r-D), and the ratio between r and D of 2.5. 1

From a manufacturing standpoint, it would be very expensive to make the working surface of the head of the stud-conform to the theoretical curve, as expressed in Equation (VI), because of the special nature of machines and tools which would be required to conform the working surface to a curve corresponding to that of Equation (VI) as well as because of the precision of workmanship which would be required.

Therefore, in actual practice, the working surface of the stud deviates slightly from the exact curve defined by Equation (VI), but such deviation is of such inappreciable extent that the beneficial effects of the theoretical type of curve are in solid lines.

of my insulator stud is shown diagrammatically.

The theoretical curve corresponding to Equation (VI) is shown by the broken line, and a curve. representing the actual curve for the working surface of the stud, which I employ, is shown It should be understood that, for purposes of clarity, the degree of non-conformity of the actual and the theoretical curves is exaggerated. As a matter of fact, the actual curve is not ordinarily visibly different from the theo retical curve. The radius of curvature R ofthe actual curve which I employ is empirically determined as is the center of curvature 0 from which the arc is struck, by selecting that value of R and that position of the center 0 which will permit the arc to conform most'colsely to the particular theoretical curve previously selected.

The working surface of the stud is thus that which is generated by the revolution of the arc of constant radius of curvature, so attained, about the longitudinal axis of the stud.

In Fig. 3, the y-axis, the m-axis (1) and the :caxis (2) are shown in positions corresponding to those indicated in Fig. 2. Another axis is shown in Fig. 3, namely, :c-axis (3) which lies in a plane perpendicular to the y-axis and intersecting the upper extremity of the working surface of the stud. The distance between m-axis '(2) and :c-axis' (3) is designated by the character Y. The distance from .r-axis (2) to the lower extremity of'the cementitious material is designated by the character H. The distance from the y-axis, that is, the longitudinal axis of the stud, to the most remote point on the working surface parallel to the :r-axes, is designated by the character X.

The-radius of curvature of the locus of the center of curvature 0 of the working surface for a revolution of the arc generating it, is a circle disposed in a plane perpendicular to the axis of the stud, and having a radius w. The distance between the plane in which the locus of the center of curvature 0 is disposed and x-axis (3) is designated by the character h.

As previously mentioned, the theoretical curve selected and plotted in Fig. 2, upon the basis of r being equal to 2.5D, and my being equal to .(r-D) resulted in the attaining of a working such as R, w and h maybe obtained in terms of the radius of the shank D by trigonometric solutions. It is first necessary, however, to obtain the angle 62 between the tangent to the actual curve employed for the working surface at the intersection thereof with the shank of the stud and a line parallel to the y-axis, also passing through the intersection of the working surface and the shank of the stud, from the slope of the tangent line at the intersection.

It should be understood that, in the practical design of my insulator, the lower extremity of the cementitious material interposed between the section of y-axis and x-axis ('2).

produced byan axial movement of the stud create a radially expansive force on the porcelain or dielectric member, tending to burst it. The cap member 4 is, therefore, designed so that it sets up reactive "forces which neutralize those produced by the stud. More particularly, the cap member has a curvature on its inner surface which produces a radial crushing force on the dielectric member at least as great as the radial outward force caused by the stud. By extending the radius of the stud working surface curvature at the intersection of the working surface and the shank of the stud to a point on the outside surface of the porcelain, as indicated by the brokenjline R2, and considering-this point as on a level'with the lower tip of the cap member, then the radial component of force of the cap should be equal to, or greater than, the radial force set up by the stud.

Representing as 94, the angle subtended by the tangent to the working surface of the cap member at the lower extremity, and a line parallel to the y-axis or axis of the stud, 64 should, therefore, be not greater than 92. The amount that 64 is less than 92 depends partly upon the value of Y, and partly upon the desired proportion of stress created by the cap member with respect to that created by the stud. The exact curvature and dimensions of the cap is influenced also toa large extent, by the electrical field conditions around the outside of the insulator. From a mechanical stress point of view, it is desirable to have the working surface of the cap member continually taper outward from the porcelain. This, of course, cannot be done in a practical design.

I obtain the curve of the lower inner surface of the cap member in a practical manner by striking an arc of constant radius of curvature Rx from a center of curvature, located somewhere on the y-axis such, for example, as the inter- The angle 64 is thus less than the angle 92. The lower extremityof the working surface of the cap member is obtained by revolving the arc of constant radius of curvature R about the axis of the stud, that is, y-axi s.

In determining the, comparative tensile strengths of. insulators constructed in accordance with the principles of my invention, and other insulators widely known' and used at the present time, large numbers of insulators of each type maximum and minimum tensile strength values' of a similar number of any other known type of insulators.

Thus, it will be clearly seen that insulators constructed according to the principles of my invention are more consistent in the tensile strength values obtainable therefrom. It will be understood that no matter how carefully the various elements of insulators are manufactured and assembled, there is, nevertheless, a suflicient variation in the cooperative relation of the various parts, so that an absolutely consistent value oftensile strength cannot be obtained. By constructing insulators according to the principles of my invention, the variation between the maximum and minimum values of tensile strength obtainable in a large group of insulators is reduced to a mmimum.

The results of the above-mentioned tests also indicate-that a large number of insulators, con-' .structed in accordance with the principles of my invention, are capable of withstanding a predetermined high tensile force than any other known type of insulator of corresponding weight. In other words, the median value of tensile strength obtainable by constructing an'insulator in ac c'ordance with my invention, is higher than that obtainable by any other known type of insulator of corresponding weight.

It has also been determined from tests of large numbers of insulators of corresponding weight, that the average value of tensile strength attainable by insulators constructed according to my invention, is considerably higher than the average value attainable by the best of other known types of insulators of corresponding weight. It has, furthermore, been determined that the minimum value of tensile strength of insulators constructed in accordance with the principles of my invention is higher than the minimum value obtained from a large group of the best type of other insulators of corresponding weight.

It will thus be seen that my invention possesses distinct advantages from a commercial viewpoint, and that it representsa distinct advance in the art of suspension insulators, because of the simplicity of manufacture of insulators in' accordance therewith as well as because of the general increase in tensile strength obtainable and the consistency with which a predetermined maxiwhereby a substantially straight-walled cavity in a dielectric member may be employed, and a maximum equalization of stresses in the cementitious and dielectric materials, interposed between the working surfaces of the stud and the cap member of an insulator, is effected.

Obviously, my invention is capable of certain modifications, such as employing a multi-step working surfacefor the load-supporting stud, without departing from the spirit thereof. I do not, therefore, intend to limit my invention to the specific embodiment shown and described in the foregoing specification, but consider that other embodiments, constructed in accordance with the principles of my invention, are included within the scope thereof;

Furthermore, I do not intend to limit the scope of my invention, except as necemitatedby the prior art and as defined in the appended claims.

- I claim as myinvention:

1. In an insulator, a dielectric member having a cavity therein, a load member adapted to be retained within the cavity by a compressible medium adhering to said dielectric member, said load member having a working surface and a shank, a portion of its working surface/being generated by the revolution of a curve about the axis of the load member, which curve conformssubstantially to that represented by the expression :c--D y 'z z g;

in which 1 represents the y-coordinate of the curve with respect to an x-axis of coordinates lying in the plane of the intersection of the working surface and shank of the load member, :n represents the x-coordinate with respect to a y-axis coincident with the longitudinal axis of the load member, yo designates the theoretical 'depth of compressible medium, parallel to the axis of the load member, below the intersection of the working surface and shank of the load member, designates the radial distance parallel to the x-axis from the y-axis to a hypothetical neutral boundary of compressive forces, and D designates the radius of the shank of the load member.

2. In an insulator, a dielectric member having a cavity therein, a load member adapted to be disposed at least partly within the cavity, ce-q mentitious material for retaining said load member in co-operative relation with the cavity, said load member having a working surface to which said cementitionus material is conformed, and at least a portion of the said working surface being generated by the revolution about the axis of the load member in'concave relation thereto, of an arc of substantially constant radius of curvature, the are having aradius of curvature and a position for its center 'of curvature such that it conforms closely to the curve in which 1 represents the y-coordinate of the curve with respect to an :c-axis of coordinates lying in the plane of the intersection of the working surface and shank of the load membenzr represents the :c-coordinate with respect to a y-axis coincident with the longitudinal axis of the load member, 1/0 designates the theoretical depth of compressible medium, parallel to the axis of the load member, below the intersection of the working surface and shank of the load member, 1' designates the radial distance parallel to the :c-axis from the y-axis to a'hypothetical neutral boundary of compressive forces, and D designates the radius of the shank of the load member.

3. In an insulator, a dielectric member having a substantially cylindrical'cavity therein, a load member having'a working surface adapted to be retained within the cavity, the working surface of the load member bearing a relation to the wall surfaces of the cavity such that it effects an equalization of compressive stresses in the dielectric member and being generated by the revolution about the axis of the load member in concave relation thereto of an arc of substantially constant radius of curvature, with the arc and its center of curvature on. opposite sides of the axis, and a cap member having a working surface in external relation to the dielectric member adapted to effect a reactive compressive force to that set up by the load member in the dielectric member upon the imposition of an axial spect to the dielectric member, the working surface of said cap member being generated by the revolution, about an axis coincident with that of the load member in concave relation thereto, of an arc of substantially constant radius of curvature.

4. An insulator comprising adielectric memher having a cavity therein, a load member adapted to be retained within the cavity, and a cap member adapted to be secured in external relation to the dielectric member, said load member and said cap member having working surfaces which bear a relation adapted to eifect substantially equal compressive stresses in different parts of said dielectric member when a tensile force is exerted tending to separate said load and cap members, the Working surface of said load member including at least a portion generated by the revolution about the axis of the load member in concave relation thereto of an arc of substantially constant radius of curvature, the arc and its center of curvature being on opposite sides respectively of the axis, the working surface of the cap member including a portion generated by the revolution about an axis coincident with that of the load member in concave relation thereto of an arc of substantially constant radius of curvature.

5. In an insulator, a dielectric member having a cavity therein, a load member having a working surface adapted to be retained within the cavity and having a shank portion intersected by the working surface thereof, and a cap member having 'a working surface and adapted 'to be secured thereby in external relation to the dielectric member, the working surfaces of said load member and said cap member bearing a relation adapted to effect substantially equal compressive stresses in different parts of said dielecrelation thereto of an arc of substantially constant radius of curvature with the arc and its center of curvature on opposite sides of the axis, the working surface of the said cap member being generated at least in a portion thereof by the revolution about an axis coincident with the axis of the load member in concave relation thereto of an arc of substantially constant radius of curvature, the angle at the intersection of the working surface and shank of the load member being greater than that between any portion of the curve of the working surface of the cap member and an axis parallel to the axis of the load member.

,EDWIN E. ARNOLD. 

